A336406 a(n) = number of primes c + d, where c < d = odd composite(n), and c is composite.

2, 3, 4, 6, 6, 7, 7, 8, 9, 10, 10, 13, 13, 12, 12, 13, 14, 14, 14, 16, 16, 18, 18, 17, 19, 18, 17, 20, 21, 21, 23, 23, 22, 23, 24, 24, 26, 27, 27, 27, 26, 26, 29, 28, 27, 29, 28, 30, 30, 30, 31, 32, 31, 32, 33, 33, 34, 34, 33, 35, 35, 37, 37, 37, 38, 38, 40

Offset: 1

Author

Clark Kimberling, Jul 20 2020

Keywords

• nonn

Examples

			The 5th odd composite is 27, so that a(5) counts these 6 primes:
4 + 27, 10 + 27, 14 + 27, 16 + 27, 20 + 27, 26 + 27.
		

Crossrefs

Cf. A000040, A002808, A014076, A336407, A336408.

Programs

Mathematica

z = 400; p = Prime[Range[z]];
c = Select[Range[2, z], ! PrimeQ@# &];  (* A002808 *)
d = Select[Range[2, z], ! PrimeQ@# && OddQ@# &];  (* A014076 *)
f[n_] := Select[c, # < d[[n]] &];
g[n_] := d[[n]] + Select[c, # < d[[n]] &];
q[n_] := Length[Intersection[p, g[n]]];
tq = Table[q[n], {n, 1, 120}] (* A336406 *)
tc = Table[Length[f[n]], {n, 1, 120}] (* A336407 *)
m = Min[Length[tq], Length[tc]]; Take[tc, m] - Take[tq, m] (* A336408 *)